hktoc

Linear Equations
	Fields
	Systems of Linear Equations
	Matrices & elementary row operations
	Row-reduced Echelon Matrices
	Matrix Multiplication
	Invertible Matrices

Vector Spaces
	Vector Spaces
	Subspaces
	Bases and Dimension
	Coordinates
	Summary of Row-Equivalence
	Computations Concerning Subspaces

Linear Transformations
	Linear Transformations
	The Algebra of Linear Transformations
	Isomorphism
	Representations of Transformations by Matrices
	Linear Functionals
	The Double Dual
	The Transpose of a Linear Transformation

Polynomials
	Algebras
	The Algebra of Polynomials
	Lagrange Interpolation
	Polynomial Ideals
	The Prime Factorization of a Polynomial

Determinants
	Commutative Rings
	Determinant Functions
	Permutations and Uniqueness of Determinants
	Additional Properties of Determinants
	Modules
	Multilinear Functions
	The Grassman Ring

Elementary Canonical Forms
	Introduction
	Characteristic Values
	Annihilating Polynomials
	Invariant Subspaces
	Simultaneous Triangulation; Simultaneous Diagonalization
	Direct-sum Decompositions
	Invariant Direct Sums
	The Primary Decomposition Theorem

The Rational and Jordan Forms
	Cyclic Subspaces and Annihilators
	Cyclic Decompositions and the Rational Form
	The Jordan Form
	Computation of Invariant Factors
	Summary; Semi-Simple Operators

Inner Product Spaces
	Inner Products
	Inner Product Spaces
	Linear Functionals and Adjoints
	Unitary Operators
	Normal Operators

Operators on Inner Product Spaces
	Introduction
	Forms on Inner Product Spaces
	Positive Forms
	More on Forms
	Spectral Theory
	Further Properties of Normal Operators

Bilinear Forms
	Bilinear Forms
	Symmetric Bilinear Forms
	Skew-Symmetric Bilinear Forms
	Groups Preserving Bilinear Forms